Explain the graph sin(1/x)? It looks funny.?

Answer 1

I assume what looks 'funny' to you is the wild oscillations near x=0. The reason is that for x near zero, the quantity 1/x gets really large, and as x gets closer to zero the value of 1/x changes a LOT for a small change in x. What this means for sin(1/x) is that the sine function goes through many oscillations over just a small range of x (near zero) because its argument changes so much. Does that make sense?

See if you can make an argument for what behavior to expect for sin (1/x) when x is far from zero instead (positive or negative).

Answer 2

The graph of the sine function of course is a repeating wavy line whose values will fluctuate between 0 and 1. Since we know that division by zero is undefined, when x = zero, you get an asymptote. As X approaches 0 from 1 the value of (1/x) gets larger. As this value rises it acts just as the sine function normally does (makes a complete cycle every 360 degrees when X=(1/360)then (1/x)=360 and the value of the function should be zero since sin(360) is zero. So since you approach positive infinity as x gets smaller in absolute value you get those wavy lines between 0 and 1. The same is true for x between negative 1 and 0 except as x approaches zero from negative 1 the value of the fraction approaches negative infinity. As X>1 the value of (1/x) approaches zero (on both sides) and the value of the sin(0) is 0 which is why you see the graph on both sides approaching the X axis beyond X=1 and X=-1

Answer 3

its reasonable
just use a dummy variable to plot 1/x along with the function and you'll see it